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September, 1978 Linear Estimation for Approximately Linear Models
Jerome Sacks, Donald Ylvisaker
Ann. Statist. 6(5): 1122-1137 (September, 1978). DOI: 10.1214/aos/1176344315


An approximate linear model is proposed to allow for deviations from an underlying ideal linear model as follows: If, in standard notation, $Y = A\beta + \varepsilon$ is the ideal model then $Y = A\beta + r + \varepsilon$ where $|r_i| \leqq M_i$ for $M$ a given vector is an approximate linear model. The problem solved here is that of finding a linear estimate of a single linear function of $\beta$ which minimaxes mean square error in the approximate model. The estimate obtained may be the standard one from the ideal model, but in general it is not. The estimate is calculated as a solution to a set of nonlinear equations (generalizing the usual normal equations) and an algorithm is given for obtaining the solution.


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Jerome Sacks. Donald Ylvisaker. "Linear Estimation for Approximately Linear Models." Ann. Statist. 6 (5) 1122 - 1137, September, 1978.


Published: September, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0384.62058
MathSciNet: MR501615
Digital Object Identifier: 10.1214/aos/1176344315

Primary: 62J05
Secondary: 62J10 , 62J35

Keywords: approximately linear models , minimum mean square linear estimation , normal equations

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 5 • September, 1978
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